AI RESEARCH / HUMAN–MACHINE COLLABORATION
Fractal Context
I worked on the mathematics. AI worked on the machinery.
Fractal Context began with a speculative question: could a transformer gain something useful by applying the same simple quadratic rule to its recent context at several different scales?
Throughout the work, I did not look at the implementation. I worked on the hypothesis, the mathematical form, the controls, and the interpretation of each result. AI translated those decisions into code, ran the experiments, and returned evidence for the next decision.
The collaboration let me remain inside the problem instead of disappearing into the machinery required to test it.
A mathematical idea became a falsifiable experiment.
The experiment looks at the model’s recent past across spans of 1, 2, 4, 8, and 16 tokens, then applies one shared quadratic recurrence across those scales.
The important question is not whether this architecture can be made to run. It is whether the quadratic relationship contributes something that an unchanged baseline, an ordinary gate, and a matched linear recurrence do not.
That distinction shaped the entire experiment. Any apparent improvement has to survive controls designed to separate the quadratic idea from generic gating, extra computation, or chance.
The code was not the interface.
My interface to the project was the mathematics and the evidence.
When a result exposed ambiguity, I could reformulate the question. AI could change the implementation, add instrumentation, run the comparison, and bring the result back. I could then decide whether the behavior was meaningful, whether the control was strong enough, and what the next experiment needed to ask.
This is more consequential than using AI to write code faster. It suggests that difficult technical research can be conducted at the level where the original thinking happens, while AI handles much of the translation and experimental machinery underneath.
There is a signal, not a conclusion.
The early results contain enough promise to justify continuing.
That is not the same as saying the architecture works. The apparent effect may disappear in larger models, reverse across seeds, fail against the complete matched controls, or prove to be noise. It may be a small-scale curiosity that does not survive contact with real training conditions.
The honest conclusion is narrower: the hypothesis has earned another experiment. It has not yet earned a claim.
This is an emerging form of collaboration.
Recent work on Erdős problems offers a useful parallel. Open mathematical questions are increasingly being explored through combinations of expert problem framing, AI-assisted search, numerical experiments, formalization, literature discovery, and human proof.
The leverage comes from more than a clever prompt. It comes from expert prompting: knowing how to pose a tractable question, recognize an interesting structure, reject weak evidence, connect a result to existing knowledge, and ask the next experiment.
Fractal Context follows that pattern at a smaller experimental scale. My contribution is the mathematical direction, judgment, skepticism, and next question. AI contributes the implementation and experimental throughput that make rapid iteration possible.
The hypothesis may ultimately fail. The collaboration has already demonstrated something important: a person can pursue a difficult architecture question through direct engagement with its mathematics, while AI makes the underlying research machinery available on demand.
Owen Fowler
AI Systems Builder
Tell me what you’re working on.
A few sentences is enough.